{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a9171081",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Differentiable Cosmological Simulation with Adjoint Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2b2709ea",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NVIDIA H100 PCIe\r\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "\n",
    "# change JAX GPU memory preallocation fraction\n",
    "os.environ['XLA_PYTHON_CLIENT_MEM_FRACTION'] = '.95'\n",
    "\n",
    "import jax\n",
    "# jax.print_environment_info()\n",
    "\n",
    "!nvidia-smi --query-gpu=gpu_name --format=csv,noheader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c185a885",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "import jax.numpy as jnp\n",
    "from IPython.display import YouTubeVideo\n",
    "\n",
    "from pmwd import (\n",
    "    Configuration,\n",
    "    SimpleLCDM,\n",
    "    boltzmann,\n",
    "    white_noise, linear_modes,\n",
    "    lpt,\n",
    "    nbody,\n",
    "    scatter,\n",
    ")\n",
    "from pmwd.vis_util import simshow"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "722be0e3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Reproducibility\n",
    "\n",
    "GPU can output different results for identical inputs. We compare the particle displacements and velocities between 2 runs,\n",
    "$\\sigma_{\\mathbf{s}_1 - \\mathbf{s}_2} / \\sigma_{\\mathbf{s}_1}$ and $\\sigma_{\\mathbf{p}_1 - \\mathbf{p}_2} / \\sigma_{\\mathbf{p}_1}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "99d08f34",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def check_reproducibility(\n",
    "        ptcl_spacing,\n",
    "        mesh_shape,\n",
    "        a_nbody_maxstep,\n",
    "        float_dtype,\n",
    "        ptcl_grid_shape=(384,) * 3,\n",
    "        seed=0,\n",
    "    ):\n",
    "    conf = Configuration(\n",
    "        ptcl_spacing,\n",
    "        ptcl_grid_shape,\n",
    "        mesh_shape=mesh_shape,\n",
    "        a_nbody_maxstep=a_nbody_maxstep,\n",
    "        float_dtype=float_dtype,\n",
    "    )\n",
    "    cosmo = SimpleLCDM(conf)\n",
    "    modes = white_noise(seed, conf)\n",
    "\n",
    "    def model(modes, cosmo, conf):\n",
    "        cosmo = boltzmann(cosmo, conf)\n",
    "        modes = linear_modes(modes, cosmo, conf)\n",
    "        ptcl, obsvbl = lpt(modes, cosmo, conf)\n",
    "        ptcl, obsvbl = nbody(ptcl, obsvbl, cosmo, conf)\n",
    "        return ptcl, obsvbl\n",
    "\n",
    "    p1, _ = model(modes, cosmo, conf)\n",
    "    p2, _ = model(modes, cosmo, conf)\n",
    "    disp_std = p1.disp.std()\n",
    "    vel_std = p1.vel.std()\n",
    "    print(f'{float_dtype}, {mesh_shape**3}, {cosmo.ptcl_mass :.0f}, {conf.a_nbody_num :3}'\n",
    "          f': {(p1.disp - p2.disp).std() / disp_std :.1e}'\n",
    "          f', {(p1.vel - p2.vel).std() / vel_std :.1e}'\n",
    "          f'; {disp_std :.1e}, {vel_std :.1e}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3c8b572d",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f4, 8, 1,  63: 1.9e-06, 7.1e-05; 5.1e+00, 3.3e+00\n",
      "f4, 8, 1, 126: 5.2e-07, 1.3e-05; 5.1e+00, 3.3e+00\n",
      "f4, 8, 8,  63: 3.1e-07, 2.4e-06; 5.7e+00, 3.5e+00\n",
      "f4, 8, 8, 126: 3.2e-07, 2.3e-06; 5.7e+00, 3.5e+00\n",
      "f4, 1, 1,  63: 1.4e-07, 1.5e-06; 5.1e+00, 3.2e+00\n",
      "f4, 1, 1, 126: 1.3e-07, 1.4e-06; 5.1e+00, 3.2e+00\n",
      "f4, 1, 8,  63: 1.1e-07, 4.5e-07; 5.6e+00, 3.3e+00\n",
      "f4, 1, 8, 126: 9.8e-08, 4.4e-07; 5.6e+00, 3.3e+00\n"
     ]
    }
   ],
   "source": [
    "check_reproducibility(ptcl_spacing=.5, mesh_shape=2, a_nbody_maxstep=1/64, float_dtype='f4')\n",
    "check_reproducibility(ptcl_spacing=.5, mesh_shape=2, a_nbody_maxstep=1/128, float_dtype='f4')\n",
    "check_reproducibility(ptcl_spacing=1., mesh_shape=2, a_nbody_maxstep=1/64, float_dtype='f4')\n",
    "check_reproducibility(ptcl_spacing=1., mesh_shape=2, a_nbody_maxstep=1/128, float_dtype='f4')\n",
    "check_reproducibility(ptcl_spacing=.5, mesh_shape=1, a_nbody_maxstep=1/64, float_dtype='f4')\n",
    "check_reproducibility(ptcl_spacing=.5, mesh_shape=1, a_nbody_maxstep=1/128, float_dtype='f4')\n",
    "check_reproducibility(ptcl_spacing=1., mesh_shape=1, a_nbody_maxstep=1/64, float_dtype='f4')\n",
    "check_reproducibility(ptcl_spacing=1., mesh_shape=1, a_nbody_maxstep=1/128, float_dtype='f4')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "161bc793",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "| precision | cell/ptcl | ptcl mass $[M_\\odot]$ | time steps | disp rel diff | vel rel diff |\n",
    "| --- | --- | --- | --- | --- | --- |\n",
    "| single | 8 | 1e10 |  63 | 1.6e-6 | 4.8e-5 |\n",
    "| single | 8 | 1e10 | 126 | 5.1e-7 | 1.3e-5 |\n",
    "| single | 8 | 8e10 |  63 | 3.1e-7 | 2.4e-6 |\n",
    "| single | 8 | 8e10 | 126 | 3.1e-7 | 2.3e-6 |\n",
    "| single | 1 | 1e10 |  63 | 1.4e-7 | 1.5e-6 |\n",
    "| single | 1 | 1e10 | 126 | 1.3e-7 | 1.4e-6 |\n",
    "| single | 1 | 8e10 |  63 | 1.1e-7 | 4.5e-7 |\n",
    "| single | 1 | 8e10 | 126 | 9.9e-8 | 4.4e-7 |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fd333744",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f8, 8, 1,  63: 1.2e-15, 3.0e-14; 5.4e+00, 3.5e+00\n",
      "f8, 8, 1, 126: 7.9e-16, 1.6e-14; 5.4e+00, 3.5e+00\n",
      "f8, 8, 8,  63: 5.8e-16, 4.2e-15; 5.9e+00, 3.6e+00\n",
      "f8, 8, 8, 126: 5.9e-16, 4.2e-15; 5.9e+00, 3.6e+00\n",
      "f8, 1, 1,  63: 2.4e-16, 2.3e-15; 5.4e+00, 3.4e+00\n",
      "f8, 1, 1, 126: 2.3e-16, 2.3e-15; 5.4e+00, 3.4e+00\n",
      "f8, 1, 8,  63: 2.0e-16, 7.9e-16; 5.8e+00, 3.4e+00\n",
      "f8, 1, 8, 126: 1.8e-16, 7.7e-16; 5.9e+00, 3.4e+00\n"
     ]
    }
   ],
   "source": [
    "check_reproducibility(ptcl_spacing=.5, mesh_shape=2, a_nbody_maxstep=1/64, float_dtype='f8')\n",
    "check_reproducibility(ptcl_spacing=.5, mesh_shape=2, a_nbody_maxstep=1/128, float_dtype='f8')\n",
    "check_reproducibility(ptcl_spacing=1., mesh_shape=2, a_nbody_maxstep=1/64, float_dtype='f8')\n",
    "check_reproducibility(ptcl_spacing=1., mesh_shape=2, a_nbody_maxstep=1/128, float_dtype='f8')\n",
    "check_reproducibility(ptcl_spacing=.5, mesh_shape=1, a_nbody_maxstep=1/64, float_dtype='f8')\n",
    "check_reproducibility(ptcl_spacing=.5, mesh_shape=1, a_nbody_maxstep=1/128, float_dtype='f8')\n",
    "check_reproducibility(ptcl_spacing=1., mesh_shape=1, a_nbody_maxstep=1/64, float_dtype='f8')\n",
    "check_reproducibility(ptcl_spacing=1., mesh_shape=1, a_nbody_maxstep=1/128, float_dtype='f8')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3499bcfe",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "| precision | cell/ptcl | ptcl mass $[M_\\odot]$ | time steps | disp rel diff | vel rel diff |\n",
    "| --- | --- | --- | --- | --- | --- |\n",
    "| double | 8 | 1e10 |  63 | 1.4e-15 | 3.6e-14 |\n",
    "| double | 8 | 1e10 | 126 | 8.3e-16 | 1.7e-14 |\n",
    "| double | 8 | 8e10 |  63 | 5.4e-16 | 4.1e-15 |\n",
    "| double | 8 | 8e10 | 126 | 5.9e-16 | 4.3e-15 |\n",
    "| double | 1 | 1e10 |  63 | 2.4e-16 | 2.3e-15 |\n",
    "| double | 1 | 1e10 | 126 | 2.3e-16 | 2.3e-15 |\n",
    "| double | 1 | 8e10 |  63 | 1.9e-16 | 7.9e-16 |\n",
    "| double | 1 | 8e10 | 126 | 1.8e-16 | 7.8e-16 |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36bbc1de",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Reversibility\n",
    "\n",
    "Model differentiation evolves the adjoint equations backward in time. To save memory, trajectory of the model state in the forward run is not saved, but re-simulated together with the adjoint equations. Even though in principle the N-body systems are reversible, in practice the re-simulated trajectory can differ from the forward one due to loss of small-scale information.\n",
    "\n",
    "We compare the displacements and velocities of particles that have evolved to the final time (a=1) and then back, to those of the LPT initial conditions (a=1/64),\n",
    "$\\sigma_{\\mathbf{s}_{rev} - \\mathbf{s}_{LPT}} / \\sigma_{\\mathbf{s}_{LPT}}$ and $\\sigma_{\\mathbf{p}_{rev} - \\mathbf{p}_{LPT}} / \\sigma_{\\mathbf{p}_{LPT}}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "64667860",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def check_reversibility(\n",
    "        ptcl_spacing,\n",
    "        mesh_shape,\n",
    "        a_nbody_maxstep,\n",
    "        float_dtype,\n",
    "        ptcl_grid_shape=(384,) * 3,\n",
    "        seed=0,\n",
    "    ):\n",
    "    conf = Configuration(\n",
    "        ptcl_spacing,\n",
    "        ptcl_grid_shape,\n",
    "        mesh_shape=mesh_shape,\n",
    "        a_nbody_maxstep=a_nbody_maxstep,\n",
    "        float_dtype=float_dtype,\n",
    "    )\n",
    "    cosmo = SimpleLCDM(conf)\n",
    "    modes = white_noise(seed, conf)\n",
    "\n",
    "    cosmo = boltzmann(cosmo, conf)\n",
    "    modes = linear_modes(modes, cosmo, conf)\n",
    "    p0, obsvbl = lpt(modes, cosmo, conf)\n",
    "\n",
    "    p1, obsvbl = nbody(p0, obsvbl, cosmo, conf)\n",
    "    p1, _ = nbody(p1, obsvbl, cosmo, conf, reverse=True)\n",
    "    disp_std = p0.disp.std()\n",
    "    vel_std = p0.vel.std()\n",
    "    print(f'{float_dtype}, {mesh_shape**3}, {cosmo.ptcl_mass :.0f}, {conf.a_nbody_num :3}'\n",
    "          f': {(p1.disp - p0.disp).std() / disp_std :.1e}'\n",
    "          f', {(p1.vel - p0.vel).std() / vel_std :.1e}'\n",
    "          f'; {disp_std :.1e}, {vel_std :.1e}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "95155318",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f4, 8, 1,  63: 4.4e-02, 7.0e-02; 1.0e-01, 6.9e-03\n",
      "f4, 8, 1, 126: 2.2e-02, 3.7e-02; 1.0e-01, 6.9e-03\n",
      "f4, 8, 8,  63: 3.4e-03, 7.8e-03; 1.1e-01, 7.7e-03\n",
      "f4, 8, 8, 126: 3.6e-03, 6.9e-03; 1.1e-01, 7.7e-03\n",
      "f4, 1, 1,  63: 1.4e-03, 2.2e-03; 1.0e-01, 6.9e-03\n",
      "f4, 1, 1, 126: 1.3e-03, 1.7e-03; 1.0e-01, 6.9e-03\n",
      "f4, 1, 8,  63: 4.5e-04, 7.7e-04; 1.1e-01, 7.7e-03\n",
      "f4, 1, 8, 126: 4.1e-04, 5.8e-04; 1.1e-01, 7.7e-03\n"
     ]
    }
   ],
   "source": [
    "check_reversibility(ptcl_spacing=.5, mesh_shape=2, a_nbody_maxstep=1/64, float_dtype='f4')\n",
    "check_reversibility(ptcl_spacing=.5, mesh_shape=2, a_nbody_maxstep=1/128, float_dtype='f4')\n",
    "check_reversibility(ptcl_spacing=1., mesh_shape=2, a_nbody_maxstep=1/64, float_dtype='f4')\n",
    "check_reversibility(ptcl_spacing=1., mesh_shape=2, a_nbody_maxstep=1/128, float_dtype='f4')\n",
    "check_reversibility(ptcl_spacing=.5, mesh_shape=1, a_nbody_maxstep=1/64, float_dtype='f4')\n",
    "check_reversibility(ptcl_spacing=.5, mesh_shape=1, a_nbody_maxstep=1/128, float_dtype='f4')\n",
    "check_reversibility(ptcl_spacing=1., mesh_shape=1, a_nbody_maxstep=1/64, float_dtype='f4')\n",
    "check_reversibility(ptcl_spacing=1., mesh_shape=1, a_nbody_maxstep=1/128, float_dtype='f4')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1ff349b",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "| precision | cell/ptcl | ptcl mass $[M_\\odot]$ | time steps | disp rel diff | vel rel diff |\n",
    "| --- | --- | --- | --- | --- | --- |\n",
    "| single | 8 | 1e10 |  63 | 5.2e-2 | 7.1e-2 |\n",
    "| single | 8 | 1e10 | 126 | 2.1e-2 | 3.6e-2 |\n",
    "| single | 8 | 8e10 |  63 | 3.3e-3 | 7.6e-3 |\n",
    "| single | 8 | 8e10 | 126 | 3.7e-3 | 7.0e-3 |\n",
    "| single | 1 | 1e10 |  63 | 1.4e-3 | 2.2e-3 |\n",
    "| single | 1 | 1e10 | 126 | 1.3e-3 | 1.7e-3 |\n",
    "| single | 1 | 8e10 |  63 | 4.3e-4 | 7.3e-4 |\n",
    "| single | 1 | 8e10 | 126 | 4.4e-4 | 6.3e-4 |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7d57a06a",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f8, 8, 1,  63: 6.0e-11, 1.5e-10; 1.1e-01, 7.4e-03\n",
      "f8, 8, 1, 126: 3.6e-11, 6.9e-11; 1.1e-01, 7.4e-03\n",
      "f8, 8, 8,  63: 5.8e-12, 1.4e-11; 1.2e-01, 8.0e-03\n",
      "f8, 8, 8, 126: 6.5e-12, 1.2e-11; 1.2e-01, 8.0e-03\n",
      "f8, 1, 1,  63: 2.2e-12, 3.5e-12; 1.1e-01, 7.4e-03\n",
      "f8, 1, 1, 126: 2.1e-12, 2.8e-12; 1.1e-01, 7.4e-03\n",
      "f8, 1, 8,  63: 7.0e-13, 1.2e-12; 1.2e-01, 8.0e-03\n",
      "f8, 1, 8, 126: 7.1e-13, 9.9e-13; 1.2e-01, 8.0e-03\n"
     ]
    }
   ],
   "source": [
    "check_reversibility(ptcl_spacing=.5, mesh_shape=2, a_nbody_maxstep=1/64, float_dtype='f8')\n",
    "check_reversibility(ptcl_spacing=.5, mesh_shape=2, a_nbody_maxstep=1/128, float_dtype='f8')\n",
    "check_reversibility(ptcl_spacing=1., mesh_shape=2, a_nbody_maxstep=1/64, float_dtype='f8')\n",
    "check_reversibility(ptcl_spacing=1., mesh_shape=2, a_nbody_maxstep=1/128, float_dtype='f8')\n",
    "check_reversibility(ptcl_spacing=.5, mesh_shape=1, a_nbody_maxstep=1/64, float_dtype='f8')\n",
    "check_reversibility(ptcl_spacing=.5, mesh_shape=1, a_nbody_maxstep=1/128, float_dtype='f8')\n",
    "check_reversibility(ptcl_spacing=1., mesh_shape=1, a_nbody_maxstep=1/64, float_dtype='f8')\n",
    "check_reversibility(ptcl_spacing=1., mesh_shape=1, a_nbody_maxstep=1/128, float_dtype='f8')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a761978",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "| precision | cell/ptcl | ptcl mass $[M_\\odot]$ | time steps | disp rel diff | vel rel diff |\n",
    "| --- | --- | --- | --- | --- | --- |\n",
    "| double | 8 | 1e10 |  63 | 5.4e-11 | 1.3e-10 |\n",
    "| double | 8 | 1e10 | 126 | 3.5e-11 | 7.0e-11 |\n",
    "| double | 8 | 8e10 |  63 | 5.8e-12 | 1.4e-11 |\n",
    "| double | 8 | 8e10 | 126 | 6.4e-12 | 1.2e-11 |\n",
    "| double | 1 | 1e10 |  63 | 2.2e-12 | 3.4e-12 |\n",
    "| double | 1 | 1e10 | 126 | 2.1e-12 | 2.9e-12 |\n",
    "| double | 1 | 8e10 |  63 | 7.2e-13 | 1.2e-12 |\n",
    "| double | 1 | 8e10 | 126 | 6.9e-13 | 9.4e-13 |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6359ced8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## A toy problem\n",
    "\n",
    "16×27×16=6912 particles, in a 160 × 270 × 160 Mpc$^3/h^3$ box, evolving with a 2× mesh (32×54×32) from $a=1/64$ to $a=1$ to match the 2D projection to the target image below at 4× resolution (64×108)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1262574a",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from PIL import Image, ImageFont, ImageDraw\n",
    "\n",
    "\n",
    "text = 'pmwd'\n",
    "font = ImageFont.truetype('../nova/NovaRoundSlim-BookOblique.ttf', 32)\n",
    "\n",
    "ptcl_spacing = 10.\n",
    "ptcl_grid_shape = (16, 27, 16)\n",
    "mesh_shape = (32, 54, 32)\n",
    "im_shape = (64, 108)\n",
    "xy = (52, 28)\n",
    "\n",
    "im = Image.new('L', im_shape[::-1], 255)\n",
    "draw = ImageDraw.Draw(im)\n",
    "draw.text(xy, text, font=font, anchor='mm')\n",
    "\n",
    "# normalize the image to make the target\n",
    "im_tgt = 1 - jnp.asarray(im) / 255\n",
    "im_tgt *= jnp.prod(jnp.array(ptcl_grid_shape)) / im_tgt.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ec7a9422",
   "metadata": {
    "hide_input": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zb4R+qqX8fUF291pNgSto/TYRwOC15RTB+n8TfALGxKyGMTGrYUzMahgTsxrGxKyGMTGrYUzMahgTsxrGxKyGMTGrYUzMahgTsxrGxKyGMTGrYUzMaji1xP4XSQ7pWE7aujUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=216x128>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "im.resize((216, 128))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8cc458ba",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from functools import partial\n",
    "\n",
    "from jax.example_libraries.optimizers import adam\n",
    "\n",
    "\n",
    "def model(modes, cosmo, conf):\n",
    "    modes = linear_modes(modes, cosmo, conf)\n",
    "    ptcl, obsvbl = lpt(modes, cosmo, conf)\n",
    "    ptcl, obsvbl = nbody(ptcl, obsvbl, cosmo, conf)\n",
    "    dens = scatter_2d(ptcl, conf)\n",
    "    return dens\n",
    "\n",
    "def scatter_2d(ptcl, conf):\n",
    "    dens = jnp.zeros(tuple(2*s for s in conf.mesh_shape), dtype=conf.float_dtype)\n",
    "    dens = scatter(ptcl, conf, mesh=dens, val=1, cell_size=conf.cell_size / 2)\n",
    "    return dens.sum(axis=2)\n",
    "\n",
    "pmwdshow = partial(simshow, figsize=(27/4, 4), cmap='cividis', colorbar=False)\n",
    "\n",
    "def obj(tgt, modes, cosmo, conf):\n",
    "    dens = model(modes, cosmo, conf)\n",
    "    return (dens - tgt).var() / tgt.var()\n",
    "\n",
    "obj_valgrad = jax.value_and_grad(obj, argnums=1)\n",
    "\n",
    "# def optim(tgt, modes, cosmo, conf, iters=100, lr=1e-3):\n",
    "#     tgt = jnp.asarray(tgt)\n",
    "#     for i in range(iters):\n",
    "#         value, modes_grad = obj_valgrad(tgt, modes, cosmo, conf)\n",
    "#         modes = modes - lr * modes_grad.conj()\n",
    "#     return value, modes\n",
    "\n",
    "def optim(tgt, modes, cosmo, conf, iters=100, lr=0.1):\n",
    "    init, update, get_params = adam(lr)\n",
    "    state = init(modes)\n",
    "\n",
    "    def step(i, state, tgt, cosmo, conf):\n",
    "        modes = get_params(state)\n",
    "        value, grads = obj_valgrad(tgt, modes, cosmo, conf)\n",
    "        state = update(i, grads, state)\n",
    "        return value, state\n",
    "\n",
    "    tgt = jnp.asarray(tgt)\n",
    "    for i in range(iters):\n",
    "        value, state = step(i, state, tgt, cosmo, conf)\n",
    "\n",
    "    modes = get_params(state)\n",
    "    return value, modes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "504f4288",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "conf = Configuration(ptcl_spacing, ptcl_grid_shape, mesh_shape)\n",
    "cosmo = SimpleLCDM(conf)\n",
    "seed = 0\n",
    "modes = white_noise(seed, conf, real=True)\n",
    "cosmo = boltzmann(cosmo, conf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f7e7bf1",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "LPT ICs at a=1/64."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "28e15bb9",
   "metadata": {
    "cell_style": "center",
    "hide_input": false
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/plain": [
       "<Figure size 648x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ptcl, obsvbl = lpt(linear_modes(modes, cosmo, conf), cosmo, conf)\n",
    "fig, ax = pmwdshow(scatter_2d(ptcl, conf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba89dc51",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Time integration for 63 steps to a=1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9eb5253c",
   "metadata": {
    "hide_input": false
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/plain": [
       "<Figure size 648x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ptcl, obsvbl = nbody(ptcl, obsvbl, cosmo, conf)\n",
    "fig, ax = pmwdshow(scatter_2d(ptcl, conf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "871b5696",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Reverse the arrow of time and integrate backward to a=1/64."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "863c0ec1-1767-4843-a6e7-5e67378018f1",
   "metadata": {
    "hide_input": false
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/plain": [
       "<Figure size 648x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ptcl, obsvbl = nbody(ptcl, obsvbl, cosmo, conf, reverse=True)\n",
    "fig, ax = pmwdshow(scatter_2d(ptcl, conf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "964b0e3b",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Here's a [YouTube video](https://www.youtube.com/watch?v=Epsgh6vr0qs) for this forward and then reverse time integration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6f8cd97d",
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"648\"\n",
       "            height=\"384\"\n",
       "            src=\"https://www.youtube.com/embed/Epsgh6vr0qs?autoplay=1\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            allow=\"autoplay\"\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x15549ab127d0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('Epsgh6vr0qs', width=648, height=384, allow_autoplay=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d1721b5",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "After 1 iteration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "49298bd6",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array(1.127, dtype=float32),\n",
       " Array(1.004, dtype=float32),\n",
       " Array(1.006, dtype=float32))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss, modes_optim = optim(im_tgt, modes, cosmo, conf, iters=1)\n",
    "loss, modes.std(), modes_optim.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f53c1dfb",
   "metadata": {
    "hide_input": true
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/plain": [
       "<Figure size 648x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pmwdshow(model(modes_optim, cosmo, conf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efabe1d9",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Optimize for an interesting objective at a=1. After 10 iteration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7e3fc1ea",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array(0.793, dtype=float32),\n",
       " Array(1.004, dtype=float32),\n",
       " Array(1.027, dtype=float32))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss, modes_optim = optim(im_tgt, modes, cosmo, conf, iters=10)\n",
    "loss, modes.std(), modes_optim.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "3eba4a01",
   "metadata": {
    "hide_input": true
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/plain": [
       "<Figure size 648x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pmwdshow(model(modes_optim, cosmo, conf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9839f210-1ba6-4edd-a22e-cc3cb9e3961a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "After 30 iteration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "98ea01af-8b60-4c50-9a4f-214b486707ea",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array(0.49, dtype=float32),\n",
       " Array(1.004, dtype=float32),\n",
       " Array(1.076, dtype=float32))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss, modes_optim = optim(im_tgt, modes, cosmo, conf, iters=30)\n",
    "loss, modes.std(), modes_optim.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "7eab4db2-813e-4a11-8ab4-2d9b5cd13bd8",
   "metadata": {
    "hide_input": true
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/plain": [
       "<Figure size 648x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pmwdshow(model(modes_optim, cosmo, conf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c73189f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "After 100 iteration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "273af0c5-4792-4817-8cf6-a61f8d3580fb",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array(0.361, dtype=float32),\n",
       " Array(1.004, dtype=float32),\n",
       " Array(1.115, dtype=float32))"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss, modes_optim = optim(im_tgt, modes, cosmo, conf, iters=100)\n",
    "loss, modes.std(), modes_optim.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "408b3c19-42f7-46db-8123-764bd086ae14",
   "metadata": {
    "hide_input": true
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/plain": [
       "<Figure size 648x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pmwdshow(model(modes_optim, cosmo, conf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eabe621a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "After 300 iteration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "bab021e5",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array(0.24, dtype=float32),\n",
       " Array(1.004, dtype=float32),\n",
       " Array(1.165, dtype=float32))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss, modes_optim = optim(im_tgt, modes, cosmo, conf, iters=300)\n",
    "loss, modes.std(), modes_optim.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "948981d8",
   "metadata": {
    "hide_input": true
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/plain": [
       "<Figure size 648x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pmwdshow(model(modes_optim, cosmo, conf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1730c865",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "After 1000 iteration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "142fb129",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array(0.264, dtype=float32),\n",
       " Array(1.004, dtype=float32),\n",
       " Array(1.223, dtype=float32))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss, modes_optim = optim(im_tgt, modes, cosmo, conf, iters=1000)\n",
    "loss, modes.std(), modes_optim.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "9627cb99",
   "metadata": {
    "hide_input": true
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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OQbn+WpW+Q/NVJKW4rtFfGDT2OVxSsNx4oYbRU2tcd7jUjI5pSpY4FOjJfinMjRnNNJW0E7jNvlnmlfcVyDQxLCmpnOD0p6bB5j0faPelVi7cmomB3YFSqpQZNNNvQTsPkjwM1A5OKnEm84NNmTC8U5K6uCepGsu1fenKzN1NJHCSu40jNg4FSm0rsbXYk6UZFMRsjmnJgtVpk2FbkVDsYnJqxIyrUe8GlJJ7gm0M344oLginbATmk8qotIq6EU8Uo45NJsINPxkU0mDYqMGOKil4bingY6U0AluaHdqwLe41WOcGnONozSPjdxTmBK1K2aGREk1IG+TFR4qRcBeaUbjYscgQHNTQ/v2NV9oapIX8vpVJy2FZbhNH5b1GZOOKJXaR6eIxt96NW9A0W40Pxg0iEK2TTduG5p7r8tJN79gdg8wFs0rNuNRKuKcCAaOZ9QsixGpIqQgCo4344pQeea3WxmxMZPNGzng0Oai3OTxSbSBJk7LtFRuQRgU7JK81CQQaUnoNLU2/BTbfHXh8HvqVt/6NWvsOvjrwaP8AivPD2f8AoJ23/o1a+xa8jGfEj0MNszw/9ofH/FOf9vP/ALSrw0nmvcf2ievhv/t6/wDaVeI+XkZrpw6bpqxjW0mxuM0ZxUirTWQ9a6OV7mN0SRt605gD0qJKkArWLurGbVmNUgGpGTcOKgwfMxVkYUdaIa3QS01K7goaXzflqwUEooWzDHFS009ClqVwA4zU0OO9P+zeWcZqdLdduc01ZasLN6FObk8VL52YdmKSZNvSq+SDTla9xK60FUFM0BtxpTIDxTNpzkVL8g9RGUryKX7y89akBBHNIVA6UcvYLixgKpzULqS3FTbSRTVO04NNq6SYJ21CL92c96HJlelYc5qwka+Xu70WWw7sgIEYpgRpOlD5ZqkjlEQ6ZpP8AQyL91JzU8kgaqjvvfdS7ieKUZWHJXHuPShGHQ0A7V5piDe1O+ugraEjYHIpdxYc0qx5fBpZVCcCqJsRAhWq3lJE61RYEUisynrWalZ2Zdi0ZABsFRbcNzQFz89OJ3Cr3JuPEYK5FRqpDUI5BxUrMMVSsxO6IJeWpMYWm9Xp7DkVnvdlbaAhOeelS7xnAprAFOOtR7dgyTV3cdCbJkznimRnc2BTkPmLinInl5NN3bTQlpox7xqq571Fsyc0xpSWpTPxgUuaJVmOKL1p3BXFQbjSo+TQpITiwCgNQ2CafKAF4qFEY81MtHYpa6iudo4pYRupGXikRtlRtLUfTQcw2tSeZzSM240ijJovroO2mo9xnkUDcRinEhBSo4zV2Vyb6EedvFAUGpZoxt3A1Gi5WlbWw76XLESrUwWM9xVBXIOM09Yp5nAiDEn0p8+mgKOupLKVBwKiLgDitpPDtz9j86VCvHesOaPypSvpU+0UvhY3Ta3FVzmn9ajDZFSwYdsGri+5DRr+DVz478PH/qJ23/o1a+wq+QfCmE8e+HgO+p23/o1a+vq8vG25lY78Nfldzw79ojr4b/7ev/aVeJCTivbf2iP+Zb/7ev8A2lXiAXiujDNqmrGFe3OyQSjFKZARUGMGnbMjNdXPIx5UNJ+birEYIGTUKrk1Ju4xRDTVhLsIfmk4qw1u2zJNQR/K+anlmdlwOlNX3FoRpJsOKmWYjmqgPPPWpN4C1UXfcTVtiRpi7U8O6jrVUNluKsBxtwacXcTEJLHmo5F44p+Cee1MaQA4NU7W1Er3K4GDUokAGDQy7uRSLHnrWCTT0NG09xpYk8U4Z6mpRDgZNQyNg4FNpx1YXvoiRZgOKUkNyKg2FhkU6M7Tg01N7MTiuhMopzBgvHSo2PpUqsdmDV76E+ZXyaFIH3qk3Lmo5E3cioatqikxNu5uOlO27TmkB2DHenZDLzSSXzB3GO27iiPIpoHz1PgBaUU27jemgofBzTWfc3NM8tjz2pDVOTEkLIwI4qMUUuDWbd2WlZEyNtXmjIYcUwIcc0qqc8Vqm9jOyFXg807cDxSkACoC2G4ob5QSuOcbTkUB+OakCh0qBlwamV1qhqz0Hh6YSXOKFGaXBBqbtlbEqfu6c0wxzUWfWmvg9KvmaWhPLd6ilgTSleM1GB6VPH0wamPvbjehEGycGlcbeRRKuDlaTJIwaT00Y/MaWY1cjkQQY71W2UYwaEmtwuPQbiaa6YNOQ4NOnYFeOtW0uUnW5CozSNweKWNTTsDdg1CV0VfUYMt1pSMdKdIMdKZg4oatoC1E3seO1AY5xTxjHNNON3FJ3SuMdGhkkCjqTXqngnwxG+ya4QEdea8z07DahED/AHq+hNAtQmiI4GPlrxc6xLoUEouzkd2Dp80230MvxtDaWmjMIFAIXtXhHmeZO+fWvW/GuoKbSSItzXkCjEzH3q8nhKnh7Sd7ixjTmPGFY0gJ3ZWlkINIh217HkcPmdB4M+bxz4fLdf7Stv8A0atfYFfH3g058deHv+wnbf8Ao1a+wa4Mb8SOvC7M8P8A2hwT/wAI5/29f+0q8Pr3X9oLBHh3P/Tz/wC0q8MfCmunDx/dJmFZ/vGiNuKmjIK0wJv5pwXBxW8U07mTaasNLbSaWIgtzSyIMZpirk8UaqQaND3+/wAdKsI4xiotvy+9RqwU8nmrvyvUm19iw9v/ABCoyqjrShrh8BEYj6VsWOhPdIGkO0n1pTlCCvLYqMZSehjDy0XNRGZXPFdkvg2ORP8AWj86bJ4KSCFnWTJHaud4mi3ZM2VGdrtHJLKcYxSPHn5qfeWlxbzlPLbAPXFRl8Lg9a3v0kY8ttUKj44pd4BzUHOacBmpUnsDiicTbhimsgNNUbaC+eKq+mora6E6hRHUC4EnzU0CVmwgJ+laun6BeXrAtGyqe+KmVRLV6JFxg3sUS8S0NNGyYFdavglGjG6XB+tA8FRoCTMPzrP65R2uX9Xn2ONUKeaUPt4ra1Hw9JbgmHLAelYpgcEhwQRWkJKXwESi4/ERtlmyKcDjrTWVwcIpNSxW8srhSpGaSvcLaDQUzU3mREVs2fhjzgCz4zVu68HCGLesufxqFiaUdHuX7CTOcWVSNoqCZdp4qzdabNbE7QTiqX7zPzgj61o53RHJZhT9wAplFSnYGrk6yAjBpdwXpUIWjJrTnZHKiYfN1qOVVHTrU9taT3MgVEJz7Vo33h24tLXz5FIGM81M6kVpLcuNNvVbGVGfkqJ2yaEk4IqSKHzTTbukkSlZkSnHSjJBzVryAhprR+YdqjJp8jsHNrYiBDHmh2THFbmleGbrUXCqjc+1WtY8GTaVF5kmRWEq9NS5G/eZqqU2ua2hy8ZGeae7elMKEMQKQqRWqbSsZtK5Ihz1px29qRE+WmpE7k7QTV6pE9Q8zB5ppcE8Vq6dok985GwgVW1PTm0+bY3Ws+a75b6mnLZXsVAaQ9ab82KOaLisTgjbxULZBzSo2080rkOflqm7olKzJI13rk0x5FU4NXbO1lkT7pxVqHQxdOQWxSnNRWpUYNsyCUK5qMHnIrdbw5iTZvrPvNOe1kCIC30rNTU3ZFuDitS94dsDd6ghx0NfQemr5GghD2WvI/BOmSxyLLJGR+FepyXYSwZOny18rnzdWpCnHVI9XBLli2zxnxven+0XjDcZrlEA25Petjxe+/WHIOeaxf4RX09BKNOKS6Hl1dZO4OADxSbSRxSkGpVG0c10KN2Yt2NjwVkeOfD+f+glbf8Ao1a+w6+QPBgDeOfD5/6iVt/6NWvr+vPxqtKJ2YV3TPEP2hiR/wAI5j/p5/8AaVeHMCete5ftDYx4cz/08/8AtKvDS/NdGH/hK5jW/iMlQYWkbJ6Ugf5aZuO6uptWsYWdxGLDrQrYqwEDrUDIQSKmUWtRpp6DjIV5rU0Xw7dazOGjU7M81V0ywe/u0ixwTXsOk2Ufh/SPM2jO2uHGYn2MLL4nsdVCjzu/QzYrLSdDsdt2qeYB3rh9Z11TOfsRwme1M8Uau+pXzAOQAelc8qlTjrSw+H5ffm7yfToOrV+zHYvf8JBqKn5ZDirdj4kvftKiZyUJ5rIJ29qQNkjtXTyR7GPO+h7BaW+l6vpnCqZitec6/octjeMwU7M10fgpZBMgLEg11vjPTov7JMu0bsV5Eav1bEqk3dSO6UFUpc9rNHjGBgDvSeWT0pBnzyvvUjsU4r37LW55evQjwTkelPtYXurhYUBJJxTMNuGO9en+AfCsd2VuXXLDmuPE4iGHpurPZG9Km6kuVFvwv4AWK2W8vF+QDPNWdc17SNOha3tggkUY4rb8W682k6a1ony8Yrwm9le4u3mLk5OeteJgKdbHyeJxErR+ykd9ecaC9nTWpdv/ABJftcMY5CFzxVZ/EOpOoHmtVMvz0zQpIOcV9A4R6RPPU31Z13hvXY3Pk3pyW45rav8Aw5HefvoFGG9K85tSftqHOPmr2fQXMmnx9wBXn4x+wtUpuz6nVQ/ee7LUwNP8KRWima6UbfesPXLixt58W4XI9K6rxZrix2TW8Zw+McV5Q7O8xaRjye9PBxqVF7WoxV5Rh7kUakuuzqAImIxTF8Q3rcO5K1mvgdKaG+XGK9FpLSyOXmb1udfot7bXsgjnAyfWk8R6THGPMgXj2rmLGRoLlHBxzXqNlBDqOilnwW21xV5+xmqi2Z0017SLizycjB2nrQUI5q7qloYL9wo4BqsfmGK7kr6nI9HYaoNSWiCW6RT3NInynBqxpyb9QjC/3qpIR7H4P8M2ksEcroM4z0qP4jJbW2mNFGACB2re8PRyQaQrD+7Xn/j7UDLujLc18Zh/a18xcnL3Ue3U5YULJbnmkOPMbNWEl2ZAqsnBNSAdTX2UZO9zxZalgMWUk1qeFrQahrCQkZBNYqSEAqa7b4c2udaSQjvWOMrezw1Sot0i6MOaokez6LoFrp8aHYu7HpXCfFicQRhUwAa9L1AmG2WUHAUV4b8SNVN7NsBzg1+f5AqmJxqxU5XR7mMahS5YnCrypY0FhtqJGPlkGlONtfpHNq7Hz7RMD+64rpvBekDU7vawyM1ybMRFgV6R8LD/AKSSw71xY6s4YWU47o2w8E6iTO/tvDNvp9sXCjOPSvG/GsgXV2UdM17dr2p/ZIm3HAxXgnii4W91RnU55rw8jlXnJ1ar3PQxqgkooppGHhDCqzrhuKerOkWBRH84OetfU76HkbajYYWnkCKOTXU6T4SmfE0o+TrzVfwtprXGoqWX5Qa7/X75dL0zy4wAdtedia86dRUobs7KNOMoucjmtQmstNgMShdwFclLqsqylomwKq3l3JeXLM7Hk1B904rppw9mtdWZTnzPTRF4atcl9xY1t6FfQXV8i3QBOe9c0MYNTaZn7chBwc1pKCknF6ERk07o+g9PtbOO0RolHI7Vl+J7wWdkxU44qfw2xexTee1cx8QpmW3KqeK+Lw1HmxvI3ezPaqTtS5keZ6pMbu7aTOeapZwKVXJJzSpgnmvtbK9keG292OQbqWRwBtp+VReKiUB3ya1eistzPfU3fBIP/CceHz/1Erf/ANGLX2DXx/4Pbb478PKO+p23/o1a+wK8zG/Ekd2F2bPD/wBoj/mW/wDt6/8AaVeJIgPJr239ocZPhv8A7ev/AGlXiLqyLkV0YX+GmY1/jaByFOBTcjFCqWGTSY7Vu2zJJEkbmkkfDUIoXrRKN0igVWrSQrK52/gnT/MnWUrxXeeJp0TSSikZ21m+CLNRpIbHzYqh4oujGkiFq+Zqt18Z/hPXh7lH1PLbts3r/Wkxg5pZV33DN701jg4r6Jaas8tgTuNEQ3TqvqaRfvU+1BOoRj/aFAJHqnhLT/KSOQiui8Yj/iSH0207RrYR6RE4HOBWR4x1ENpDRA84r5NylWxcZLoz2GlGi15HkIx9oYj1pJMMeaIuGYmmt8wJFfZSZ4fUt2EX2m5RAM819B+ArEW2nAkc4rw3wfB52qKpGea+g9IH2GyB6DFfHcT1ZOgqUXuexl8Em5HmPxXuGW7KDpmvK8krnNemfEmdLy4YgjINeZdMivZyuHJgqcGrM5MU71WwBxTwxPQVGe1TxkKMkV6a1ORhapuuVz1zXsHhlnj08AjjFeXaRaG7v0x0zXsdusdjpKjGDtrys0nFQjTWrZ3YRO7k9jgfFkQFw0hNcTM29uK67xPKZmYg8Vx5GDXdhrqioswr/wAS4gUkUbTQrYPNSZG01vZNGF3cn0+H7RcKnvXp9hbGz0kknA21574ehZ9QQ44zXquoQhdCJzg7a83MJ2lGHc7sNHSUjyrWbhGvHx1zWSr/AD81Je5+3Pnn5qiKZavTV42ijilq22Pl6ZFdF4T083N0smM4Nc3KcKBXonw7iEnGMmubGVOSlKaNsPG80j1rTERNFZcDIWvA/Gt2z61LHngGvbdQvf7K09wxwCtfP3iK4+16xLKDwTXzmQUmq1Ss9Uz0MdL3YxM9hgCnKaaxyBSD7wr6lOx5TVwOfMA969f+HGmj5JsV5GT++Ue9e/eALPbo6Sgdq8bPKqp4OWu524KN6p0via7FvpD/AEr5w168+06g/Oea908YXgOlSoTzivnqdWa+kJ/vGvP4Yw3ssO5W1ZtmE7yURjYA4qMVJIuGpqck19Uzy0CjewWvVfh7aG3ZXIxmvL7BPM1CNfVq9y0Cy+z2MbgY4rys0q8tBw7nbhIXnfsU/iHdFLAlTjivGVJlZmJya9T+IE4exK55xXk9sxDHNXlMeTDKLJxjvUbH+Zg7SKWDIuFHYmkfG7NWbOIz3KADvXrJ63b2ONa6I9Y8M6THHpouFA3YzXM+Lr1mLI3auw0aU2ejYY8ba808VXwnvWC+teDhE6mJnKR6dZ8lJJHNn7xNB60U/ZxmvaSuea2NU1o6DB5+qxL2zWfGMviuk8K227VYzjvUzfLTlPsioLmmons9larZ6UjDj5a878c3qyRMucmvTL5fJ0MHPRa8O8TXhmuXTOea+XyaLq1JVfM9XFtRhynOKck0g+9R92pI49wzX1aTkzyG7IHB202M4NS7udtNMeOatrW6IvpZm14P58eeHf8AsJ23/o1a+w6+PvBfPjnw/wD9hK2/9GrX2DXm434kzuwvws8R/aFH/IuH/r5/9pV4qCGGDXtf7QnTw7/28/8AtKvDctniuzCu1JHNXV6jCQlWwKbnvSsjE5IpoHPNW73IWw/lhxVi0tzLcoDzzUOQq5FbvhiEXd+qkd6cmoxcn0HG7kkep+F4/I0rH+zXnvje8cXjKDgZr0uHbZWe3oMV5R42kWS8JX1r57LnfESqPqepiVamonNLkgmmketSQ8R802TrX0NtLnlX1G5wa2NAsDdXyNjoaymAEYNdz4CszcNuAzg1z15+ypOZtSjzTSPUdNh2aOF9Fry3xff4uHhz3r1u1KxWjo/GBXhvjVh/bcm08Zr57JVz4md/U9HGPlppLqYLkA8VGG5x604gkCo1/wCPlF96+olK+p5EUd74F0xjeJLjqa9i1eUWWibjxha5LwLYKLWOTFb/AI5mVNCdQedtfCZpW+s4+FLsz3qEVTouR41rVy2o3Um055rmZ4WhYg1bt7tkvXyepqS/2yDdX3ap8loI8WUlL3jJPNTZGzHeoiCOlDA8ULRkWudL4Tt5HvlK9M16Lr8/2XTACcHFct4BtmlmHy10nji1kis8kEDFeFi5RljI02z0qKaouR51dyvNuYnisd1G/wBqma7b5kqpI5zX0CtGNjzZvmkK+0sAKkeAhAarjhgama5Y4WkpK+oraaHYeGFijAYjmt3WdVY2hiU8Yql4MsY7hAXNL4wSOzJEZrxpuE8Uobs9GN1SucDdoRMzHuarlznipp5jKaYI8rkV7Lu3oeddIjk+YCvTPhrMsUw3CvOraLzbhYz3Net+D9Kjt4lfpxXmZjOCw8oy3Z14aMnUTXQ1PiBdq9jiM44rw6cHzWJ9a9N+IF95UexTXmCuZck1nlFBUsKl3Kxk+aoIBlc00HmpwAFwaa0Y25Feu4aHCpEllB9ou0HvX0P4IPlaQsZ/u14X4Yt/Ov1GO9e96DB5Fh6fLXyvEUk6Kps9bAR15jjPiBqPkl4w3WvJW+Zy3qa674j3bnUymeM1xqP+7BNe1lVNUcLBdzjxcnOo7DJM7qavBqR/mHFRH5a7po5os0tBtzNq0WP71e/Kq2uhIccha8W8IQF79HxxmvZ79g+hEA8ha+azqTnVpw6Hq4ONoykeT+LtS89mjzXGLgVe12ZjqciE9DWe3AFfQUYxpwSR59VuUrsVjxmuk8J2X2q7HHQ1zajcMV33gSJY5d3c1OIly0ZS6joq80jqL1Wt7MxngYrynXgBetj1r1DxVcGGAsOOK8lvpjcXBY+tcWXxbhzs6cTJX5SFRkCpfuLzUIbaKcrb+tetFpHnyQjNtYEV6F4G0x7llnUdK8/dNzKor3X4Y2aJpmWA6V5Ob4l4bBuffQ7cJTU6qL2sSSf2U0eei14PqrH+05A3rXtXjPUFs0kRa8PvpfOvXk9TXLkaapc9rJmuOeqRDJjcKeG2rxQwBUGmLkmvoNUebuSIRnJpHYscCmkHtToxjrVJvYm3U3PBXy+OPD4P/QStv/Rq19gV8heDgD458Pn/AKiVt/6NWvr2vOxytKJ24XZnh/7Q7bf+Eb9/tX/tKvElYV7Z+0T/AMy3/wBvX/tKvEFOK3wztTRlXXvssGRdnvVY5Y5FPKHr2pysu3FdT97cwWmxEOmDXWeCoiL9Wx3rkwN0mPevQ/B9iwZHxXFiZqFGV+p00Y800dprZ8rT9444rxnWrk3N22ecGva9chabSyi9cV4jq1vJbXrh1I5rzcpcXB9zrxl9CvCgYYpsqgcUqMAud1MPzE85r3eZWPMs7jJATGAK9S+FyFVO4V53ptlLd3aIEJXPpXtnhvTItJ04TNhSBmvGzarGGHdN7s78JBual0RL4i1D7EjnOBivEdcuvtWoO+c812vjTxAt7K0ETdOOK89kQhju6mtMswro0VJ7sWKqqU+XsN3dKls7Zri9jwO9NCBVya3vC9r9ovFIGcGvRm+SLkzlprmlZHtHhGA2+kpkdBWH451LdaPFu7V12hRn+zdgXoteP+P9VaLUnt/evictiq+ZSk90e1iHyULHEONtwW96keQyDFQu2cH1p6sAK+8TTZ4DvYag5waSQfOAKl2ZBNSafF516inkZokrIcdWerfDe0CQiZ16CrPj3U4riMwLjjitTw/b/ZNG3In8NedeKb0teuCe9fJUKaxWYSqPpsezOXsqCRys9uqliKoP1qxNOS55qELvOa+savp1PGvrcjp6KGcUrptFS2KeZOB71HwvUparQ9F8FphBk44rH8ezFbnarZFamnLJa2e5OOK5bX7kzynzDk151GHNinU6HbUfLRUTn/4c96lhfgioT+lPhODzXpQdpHDLVFuwA+3ofevYdGYLYAhu1eMK5imWQdq9F8M6p9pgEe7nFedmVJzjdHZhJpOxi+NpzJKVJzXGxhlXOOK7LxnbSI+/BIrlVkQwFTwa6MMl7FMyrfG0VyWYU4MRHzToyvIzSwwyTXKxIpbce1dOu6MFrodj8P7L7TfhiOM17Dc3Kadalc44rlfBWgDT7ZLiQbcjPNdDq9st7A3luCQO1fFZlXhicYl9lHuYam6dLzPFPG10LrUyw9a5z/lnitzxXbS2+oMrKcZ61ihBtBJr66jG1ONtjyaj95jVYjrSspcjjinMgK5B6Va02J764S3VCSTW689kZeh6J4E0lXgDgc10Gvaoun2rxM2OMVFocQ8PadmUgEiuD8Yayb64bY3Ga+chTlisU5P4Ueo5KjSS6nLanKLjUHlHQmoGOcUnrmgc19AlbQ81u45WxXoHgf55Bg158wxH712ngC7WK6IdsCufFJuhI1oaTR0fjeQLZle+K8ozlzXqPjJGuYyY+RjtXmMiMkhBGKzwCth7FYn+IIqg5ph4PFL0705EdzhQSa7b3VkcxYs4jLOgAyc17/4HhNto+W4+WvJ/B+iSXF6jTIQue4r1nUb6DRdJ2o4B2181nzddRwtPe56mBjyJzkeffEHUj9qdA3evNmO5ia3PEWpHUrxyDnmseKE9DXvYai6dGNO2yOCtUUpt3EXpQWxSOCjYpcbhmuq/QwEDGpY/3hxUSsAMUI2x80J2Cxv+ER5fjzw8PXU7b/0atfYFfHvhAl/Hnh0/9RO2/wDRq19hV52N+NHbhvhZ4h+0OMjw5/28/wDtKvDV+9Xuf7QuP+Kcz/08/wDtKvEQgzmurDRvSVjnrv32K2SuBUIUhuasH5VqAtls10VEZQYsX/Hyg969v8J6aE0xJiO1eMadbme9Q47171oD7dEWPHRa8LOako0YqPXc9HBRvNtkF7qMNvkSkbfeuH8QWVrreTaY3+1ReM9SKyPCrYNcjp+tT6ZJvyWoweD5KaqRepVasnLkexK/g/Uw+ApxV218HXodTIML3q4njuVgB5dJL45nKbRHivQX1tK/Kjnfsu7Oz0W00rSLXfcbfMA71ieJPGgYNBaN8nTiuMvtYub8HLkA+9ZY3Bssc1hTwEVP2lV3ZU8Tpyw0Raa4aSUyOck018yc1ECDUhkCrgV60WranA73GTBhFXcfDe2WaYlyOtcM0u5cVo6Rr82jv+671yYqm6lJxg9WdFGXLJNn0RFrlho8LLM4HFeE+PL631TXHmtyCpPaqmqeILrUxlnYZ96yoYyzZc5NedluTxwdV1ua83ub4jF+0VktERNwgHpToSD1qSZBUagCvZUeVnE3dBJKVbA6V0XhyxEsyyn1rnHTdzV6z1eaxXatZ1edppGlLlT1Pc7bxLpmm6OYJmXftxXjXifUEvNReSE/KT2rKvL64v33Fz9M1WCsBhq87B5dTws5VYu8pbnRWxDqLlewE7utOibaaYaUV6SdmcrWhNMwK1Jpsix3AZumaqnJODUirtXIqn77Enynep4gtY7Ly8jOK4zVbkXFwWTpVBlcnOTQODzWEKUYNtG06jkrMcq8c0h4PFOZuOKaDWzsjHUkXkc1e0vUnsLtWU/LnmqAYEYpGUEcVT1VtxJ2Z6FfaxY6pYBGI34rlJNAllcmHkGsiISI24Ma2bPX57UBSucVzwpSpRtT1OiVSM37w+PwrdnBxXaeGdM07TcS3+3cvrXK/wDCYTA42Vm6lrNzffdYqD6VlWpV60XCXuryLhOnB3WrPR/EnjWGOAw2DAADAxXNaH45uIbvF0x2E9zXGJ5gGWJNRy5duBg0oZfh6dLkte/UTxNSU73PXdVttO8RWnmxbfMIrgrvwle+cRECVqppusXOmrwxI9M1sQ+N5R95OamnRr0Vy09V0uU6lOprLRmUPDN5buDMML3rrdHTS9KhEz7fNFc/eeL5bwFNmKw555Z2JLnB7ZrZ0qlWNqjt6Ee0hB3jqdVr/iw3pMUTfKOOK5GeVnJJOaEtznPJoljYjgVvToqnC0UYzqucrshXnrTuAabtZetGDTQh/DcVNBcy2EoeJiKqjINPZ8jBFO6a1Fqnod7Y+Ibe5sglwQWx3qtPoceqZa3xk+lcSEkB3AnFbumeIpdMTjnFcn1dxTlS3OlVk7KexJL4Ovo2xitrRPDqWUge8xj3rOk8fTyn/V1TuvFVxeps5WpbxNSPLJWKXs4O+56Je6zpmnWf+ilQ4HavOdY8TXt9IylzsrLeWZySzk/jUXJOCKqjgqdLXd9yKmIlPTZAjFuT1p4l2GmOAg4qP73NdnM1p1OayepOQHOTSMOMLQDhcUqmr0ZOpEFweaUjPSlkGTSkbUqLdCrm14L48deH/wDsJW3/AKNWvsOvj/wSA3jjQCev9pW//oxa+wK87GLWJ2YbZnh37RH/ADLf/b1/7SrxFZMV7d+0T/zLf/b1/wC0q8PVdxrowzfs1Yyr253cdvLH2ocADIp5UBcd6jcEJXTK/UwVnsdH4UtftN0MDPNezWEAt9OIPHy15r8NrTzbjcRnmvRNauDZwMo44r5bNZupiFRR7GEXLT5jxvxm5/tpsHjNYbgMgJFaHiKbztTZic81ns42AV9HRVqSizzKr99tDoxGB0pXaMDpUQanZUiuhS0tcxe4wt6U3nNS/LikEfGajlZXMATIpjDBwaUMVOKUqW5o0a0DbcZ3pxVRyaToaUnPFSMVMNwKnVStQhSgyKnEgMfPWtoab7mctdh5i3pnNVdjBsVIlxhsZ4qZ5EZeOtDtJj2RW3Y4obaV5FLGV8z5ulSOqu3y0ldhsQoBnOalyCMUNAQMioydo96F7oPUjbhqBwaB8xpWGKz8y/IfgEZpqtg4poJp6x55qrt7E2tuNYHNLs4zTwuTikdGWjlC5GBk0EYo6GgnNQUJSg9qQc04ISaFfoDJYjtOT0q07xFOnNVA2zg08xll3dq2VkjPUZvTf0pXcDoKEQZ5p7KKaTsJtXBGyOaRkGcimscDimqxbihtbMLdR3mL0NGI+uKaYsnNI2VGKlt9StOg7CA8ClKk9KjGetPSXnFCa6g7lqCTZH81R/aAGPFRs/FR8Ac03psCbe5I7CQ8UwnaMGlhwHyelOmUOeKWrVw0RBnnNScP0qMrjinopHNRG97FPuPJ2rimbQRzUygN1pjYDYrWUepCZEFjB+7TztxwMU4qvWlwG4FSoW6jcrjVOOaQvu4AqQrtHNSRiMJnvVWewk1uVWRhyaZ0q6rKSQagmQA5FRKHVDUu5ETTlfbSKhagxEVC5tytNh+4NQ7cYpmw5qQpheatXaJdkbfglf8AiuPD5/6iVv8A+jFr7Br468FsR478PAdP7Ttv/Rq19i15uMabid2GWjPDv2if+Zb/AO3r/wBpV4gvHSvb/wBoj/mW/wDt6/8AaVeIDiujDfw0Y1/jY9Tk0P8AMQoqMHDZp/IYP6V03ujC1meo/DuWHTlEkxAHvVnx54otJYyls4LY7V5qmtTxw+XGSPpWc7yzyFpHJJ9a8r+z4yxX1mb17Hc8Ral7OISSmeQu55NKgUjmmleaQgjpXp7O9jiepIYs9KETB5pFdlHSmlyTmqvHcVnsPcBTxTt/y1Dkk07oKal2BoYyktU44So91G85waSsgd2O2ZGaix81WNwC1FjLcU5R2sEWLuJGKQnjFSBeKbtAPNNpiTRFtOc07PFTbdy8U1I/m5pcjWwc3cjCMTxUyAjjvUuAnNNDYbcKtQsJyuBZ0GGqFsHmpZZfMOMUwqCOKWrDREPQ8UEk1MqDvUUiEHis3FpXKTTY0dalBKjJpsa5PNTPjbiqitLik9bEYkwc1L5gdarAZOKcwKdKIya1BxQrLk00Ic0qHJ5pzyAcUtN2PXYjbg05WOafsDJu71GgO6lZphdNFyKJHGWpshIO1elIhyMUFsGt7Lci7tYAuOaRiKTcc008mhvTQSWozBB5qQLgZpsh+XikRmxioVkytWiZXB601lBOaQJxmm7yTgVTlp7xKXYuQRxOuDiopYkWTiowWTnNSAbhuJ5pJK+pTeliF1+amygYp7HnAprocc0pLewIbGcjBoZip4pgyDT+tQnpYprW40sWNTqQF5qE4BqRfnFVDcUtgc7eVoQh+vWkJ5wab9xqd9bitoDgg4qWJcDNRvJmpEcbacbcwO9hXYE0iqW4FRydeKdHIUGTRza6itoKQY+TUbvupXlMxxUZUis3JvYtJDlfaKejhjzUOD3ozikpNDcbk8hA6U5WDrzUKnd1p4wtaKWtyGuhteDgB488PY/6Cdt/6NWvsKvjvwcc+PPD3/YTtv8A0atfYleVjPjR34b4WeH/ALQ//Mt/9vX/ALSrw/OK9w/aHOD4b/7ev/aVeHtgiunD/wAJGFb+Ix6oG5qVUB4qJAQKkXPWu2BzSFeNEFQlcc5p7kvUe1zxUy9CkJuyaePWmGMrzT0YYwalb6jfkSKVbjFMkjC8ijgdKTJJwattNWZK0ZEM5p/UVLtXb70zyyDntU8jRXMmMHynmhjk5FK+DxSomRU2eyC/UZyaljAUc0vkNjIpNpHWqimmJ6g0mDxTWJYZqWKIM3NSToqJgVVm9w0RXik2jmn+Zk8VEhGcGn4ApRbsJpXJJDuXio1k2jBpy5FNddxzVO+6EuzFyCKYGKnmjkUjHNQ2UkKZOeKcsgY4NRgDFN6HIpczQ+VMmkwnIpjSblppYt1pAKTld6DS7iocHNT/AHhzUSrg5NPDDOKqGi1JlqMfg8UohLjNSHbinxsF69KrlV9RcztoRLlTtNSFVHNNf5myKa2TTTshNXHE+lMEmDzQW4xTdnepbd9Cku5LuDUpWmAgDijzcdaq66k2fQQjHWlMgxxUbNuNPRQetQnrZFW7gJTjFSxYHJpm1aRm21W2rF6DpG5qLzDUwZXWoXjIPFKd90EbbMWN/nGatuodBiqGMVNHKQMGlB9GVLyFZB0pQAFxTHznNAyaq+pNtCNgc0+IEUuOaQ5B4qErO5V7qwkmQ2RSKCx5q6Nhi561XbA5FNx6hfoRumKYCRUiPuODTniyMily31QXtoxitzzUrYK1EML161InJz2qo9hPuMVcHNG/nFSOR0FNKrii3YV+41sEcU0JkZpxHFIqkipauyugzoeKOTS98VIuKlK427Gz4LH/ABXXh7P/AEE7b/0atfYlfH3g4j/hO/D3/YTtv/Rq19g1wYz4kdmG2Z4d+0T/AMy3/wBvX/tKvDwpzXuH7RHXw1/29f8AtKvFlxtrpwsb00YV3abHRjjBp7LjpUQcCnCQ5ruTRyjdrBuanO0JkdacMMvNV3fBxS2HuNY54pFQUZyaazbTxUNrdj8hSMdKbhs07d3qaMqeDQkmwu0QjOae0m1cGp3iUDcDVdkL1WqWgPzIlILZNTD2qIxnPFTKuF5qYJhJoXz9oxUZk3HimSDLU9U2jNF23YLJIej7OTT2dZB1qAnccUm3aetVzdgsL5XOakADUoPy81Dv2NRpEWrJenBpvU8UxpPM4FKCUFLmTHZisDTCnpS+bmkDkGpbiylcCpAoCjbz1pQ+TVlbcPHnNJJdA1KXU0/binmPaaYSQaVrbhe+wmSeKcq4GaaGyafkYpqwMY2c0byRihqEIHWp6j6EgbavNNElNbLNxTvK4q7t7CsluM3fNU3VaYIuamA4pwi+pMmhqqMU9IVYEmoXYqeKfGxYVWj0DVaiMqg4FAGKNnzZpXxt4ot1FcaSM8VG2c4NKikHJodgelZvVXZa3JkjATNR7/nwaVJCRtpjoeoq29Fykpa6iyDPSmYx1oUletOHzms3qy9iQHK1GW2mpF9KRkBq2m1oQmhFO41Iy7h8tR42dKkjfYOaa7MBiEk7TTmAU4NRO/7zdTs+ZSUtLdRtaiFAWG2rqpiLmqn+rNWPOylVFWYntqVZk5zUkGNuDTZHzUYYgcVF1GVx2bVh8q4ORUe496ljOfvUhi3Nx0oab1QJ20YqsCMU0uV4FOMWO9Mxg80O6BWGgEnNByKduApPvGo0KNrwWf8Aiu/D3/YTtv8A0atfY1fHnguPHjrw8f8AqJ23/o1a+w68/GJqSudmGejPEf2hV3f8I57faf8A2lXiG7tXt/7QrbR4cHr9p/8AaVeHopLZrrw38JWOev8AG7jCTuqWNhnBp/ljPNNkwOldXK46mF09CSRwq8VWLbjmkLFjg0pTC5qJS5tikrbjlO7ikdCtCA5yKeTng00rrUNmRZ4oBJPFOZMU1DtNR1sxkokZRgmnLIDUTfOaQqUq1JrbYTSZZXHU0xid1RKzVPlSnvVqVyLWI2HelV88VHk5xUirt5pJ66Da0EdccimKSW5p8jbhgU1VI60pb6DW2pIQdvFQlSTU4ztqEtzRNIURo+U1IWBWomOTUqKCMmoj2RUu5GqfNmpGKkYpWIAwKSMDdzVJW0Qr31F2jbxUkLMvGeKGKqKiLknir0iydWSTsM5FQswK0rNkc1H3rOUi0gUZpWytAbBoY7qjSxXUQDNOCFqRRzVvciJ71UYp7ib7ESJg4NSOhAyKa7grkdadDOu0hq1uloQk3qRZOcVJ/DTRhnyKSVsDAprRXFu7DWGaFbFLGQRg0MmDUW6ofkxrSGk5PNK68ULnbSd76laWANuOKR02ilwB06007mPNJ7agtxFOOalEg71Gw2ikVc80k2tENpMkcgiowDu4p+RjFNUc03qxLQsCPamaiIJPFDs232pFfiqbWwrdRWOBzTo/m61Dks1PIKDiknrcGugSJzSL8o4pC5IqRCCuO9JWb0G7pajd/rTS5p20A80w9eKTuCsA5NOThxnpSpiptg25qoxuJysEygqNtMWTaMU0yYOKPlPNVfXQXqDE9aaTuNOJzwKaBsOaljQeUTUiKBShtw4qFmKtT92OoavQ6PwcP+K58P8A/YStv/Rq19e18e+C5M+OfDw/6iVt/wCjVr7Crzcc05Kx24VNRZ4h+0KoJ8OZ/wCnn/2lXio+UV7X+0Iu5vDf/bz/AO0q8WlXZHmuvC6Ukznr61GNDAnFNcc1CjHdmpC26t+e6MeWzGuoHIpNxYYp5XIpMBOalp3KTBMrSP1zRvzTsbhR0sg63ED5GKRYyTShADUqtngVSV9xN22GFdppjncanxk4NNMOGzTlF7ISfVjCNq0zdU033MCq6e9RLR2KjqrliNNy570oGeKaj44pzvjpWqskQ73EVMNStyeKj8wmpUPc0Jp6IHfdihW29KgaPDVZacDjFRs3ek7Pce2wwRjHNLkDil7Ugjyc0WtsK/cAATSsoUZFOCjIGafNGFTINNqyBXZXwX4oC7TinKdgzSB9zVFl8x6g6Ypnlk9KkkbpT0IAyafKmwu0iMw4TPeoR1qzI24VGEGM0pR10Gn3GqwzipSmVzVc/ep5kJXFTGS1uNp9BTgDFR4Jo5pyDNTuPYRWK0HJOTUmzaacwG2q5XYV9SOP72anZgRUSjIpQOeaqOisS9WIT60+IBjionbPSliO2knqO2g+dAjZFR780533HFMZdozSfkNeZIq7hzS4A4FNjfdxQ/yHNXdWuTrewFAOaaTjpT1/eCmOMHFTJaXQ15hvL8U/aAtCqAM03OWxRtuHoIn3qdJkjihhtNLu46UJWVmD7kaxse1PChTU4lXZjHNVsnfmiyQXuSMMjmoip7VM3zLxSKMdRVON2JOyIQpHNSeZxinEgnFRslTZx2He+405Y8UYI61KihetOZQ9Lkuh8xGgPWiTkcVImM7KSWMJ+NU1pYS3uNgYL1pJFy+aekOeaRxg4os+WzDrdG14LT/iuvDx/wColbf+jVr7Cr4/8Fgjxx4f/wCwlb/+jVr7ArzcarSiduFejPD/ANoZireG8f8AT1/7SrxSRyyc19f+IvB+g+LPs39t2H2r7Nu8n986bd2N33WGfujr6Vhn4QeBD/zAv/Juf/4uijiYwhysKlCUpcyPlVRQcivqofB/wIOmhf8Ak3P/APF0H4P+BD10L/ybn/8Ai6v61DzJ+ryPliMk0r19TD4QeBB00L/ybn/+LpT8IPAp66F/5Nz/APxdP63C1tRfVpXPlVBzTpCV6V9Tj4P+BB00L/ybn/8Ai6D8IPAjddC/8m5//i6PrcLWsw+ryufLCAtUyYQ819RL8IfAq9NDx/29z/8AxdB+EPgU9dD/APJuf/4uqWMppbMTw079D5ekYZyKYJCa+pP+FQ+Bf+gH/wCTc/8A8XSf8Kf8Cf8AQC/8m5//AIuh42HZi+qyPlxmBHNRL96vqg/CDwIf+YF/5Nz/APxdA+D/AIEHTQv/ACbn/wDi6TxkG9mNYaSPlwrnpShOOa+pP+FReBv+gH/5Nz//ABdL/wAKk8D/APQE/wDJuf8A+LqljaXZk/VqndHy0sfzVK5ULgda+oB8JPA46aJ/5Nz/APxdNPwi8Ck5Oh/+Tc//AMXT+u0+iY/qs+58thDjJpu7JxX1R/wqTwPjH9h8f9fc/wD8XTB8IPAgOf7C/wDJuf8A+LqXjKfRMFhp9T5ZORT8nbmvqQ/CHwKeuh/+Tc//AMXS/wDCovAuMf2H/wCTc/8A8XQsZT8w+rT8j5U3tmp4mZ/vV9Rf8Kf8Cf8AQC/8m5//AIunD4ReBl6aH/5Nz/8AxdTHGQTu7lPDSasj5ZkGDTRjPFfU5+EXgVuuh/8Ak3P/APF0g+EHgQdNC/8AJuf/AOLpvGU77MSw07Hy4VyM0gfPFfU3/CovA2Mf2H/5Nz//ABdNHwf8CA5Ghf8Ak3P/APF03jYdExfVp9T5ZbIpm49K+qj8IfAp66H/AOTc/wD8XSf8Ke8B/wDQC/8AJuf/AOLqXi4dLlLDSPlWgDNfVP8Awp7wH/0Av/Juf/4ulHwf8CDpoX/k3P8A/F1P1qHZj+ryPlbac4p4UrzX1P8A8Kh8C5z/AGH/AOTc/wD8XR/wqLwKf+YH/wCTc/8A8XVLF010Ynh5nyyXHekZ8jAr6mPwf8CHroX/AJNz/wDxdJ/wp7wH/wBAL/ybn/8Ai6bxsewfVpHyyjYpx5FfUn/CnvAf/QC/8m5//i6d/wAKh8Cj/mB/+Tc//wAXQsZDqmJ4aR8rbSTScg19Vf8ACofAv/QD/wDJuf8A+LpP+FP+BM5/sL/ybn/+LqfrdPsx/V5nywaXaWFfU3/CoPAn/QC/8m5//i6cPhF4GH/MD/8AJuf/AOLqli6fVMX1eZ8rKNppHOTzX1T/AMKg8C5z/Yf/AJNz/wDxdIfg/wCBD10L/wAm5/8A4ul9bha1mP6vK58qhiOlO5PJr6o/4U/4D/6AX/k3P/8AF0v/AAqDwJ/0Av8Aybn/APi6SxcPMPq8j5W3kDFCAhtx6V9Uf8Kf8B/9AL/ybn/+Lpf+FQ+BSMf2Hx/19z//ABdP63DrcPq8j5bYiQcUIQODX1Gvwg8CL00L/wAm5/8A4ug/B/wITn+wv/Juf/4uq+uw3syfqstrnywW+alb5hxX1L/wp7wH/wBAL/ybn/8Ai6UfCDwIOmhf+Tc//wAXU/XIdUyvq0j5ci+U/NUsrKRxX0//AMKi8Cn/AJgf/k3P/wDF0f8ACofAv/QD/wDJuf8A+Lq/rtO1rMn6tO9z5bAxzSkZGa+o/wDhUPgX/oB/+Tc//wAXS/8ACo/A2Mf2H/5Nz/8AxdCxtPsw+rT7nyqWO7FTqcLX1D/wp/wHnP8AYX/k3P8A/F0v/CovAuMf2H/5Nz//ABdKONgujG8NJnyxuw+ae26Qg19R/wDCn/An/QC/8m5//i6cPhH4GHTQ/wDybn/+LoWMp9UweGn0Pl05C4FRrndzX1P/AMKk8D/9AP8A8m5//i6b/wAKh8C5/wCQH/5Nz/8AxdN42m+jEsNPyPnjwa4Hjnw+PXUrb/0atfX1cdZ/CvwXYX9tfW2jeXc20qzRP9qmO11IIOC+DyB1rsa48TWVWSa6HTRpOmmmf//Z\n",
      "text/plain": [
       "<Figure size 648x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pmwdshow(model(modes_optim, cosmo, conf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f54679d",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "After 3000 iteration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "0f5b32e8",
   "metadata": {
    "hide_input": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array(0.196, dtype=float32),\n",
       " Array(1.004, dtype=float32),\n",
       " Array(1.366, dtype=float32))"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss, modes_optim = optim(im_tgt, modes, cosmo, conf, iters=3000)\n",
    "loss, modes.std(), modes_optim.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "297c7d65",
   "metadata": {
    "hide_input": true
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/plain": [
       "<Figure size 648x384 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = pmwdshow(model(modes_optim, cosmo, conf))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46bdae4f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Here's a [YouTube video](https://www.youtube.com/watch?v=vD6lbjHP3SY) for a similar optimization process, in which we want to match not just one but two perpendicular 2D projections to the same target image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "d185376d",
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"648\"\n",
       "            height=\"384\"\n",
       "            src=\"https://www.youtube.com/embed/vD6lbjHP3SY?autoplay=1\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            allow=\"autoplay\"\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x15549ab12cb0>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('vD6lbjHP3SY', width=648, height=384, allow_autoplay=True)"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
